AI-generated images have become increasingly realistic and have garnered significant public attention. While synthetic images are intriguing due to their realism, they also pose an important misinformation threat. To address this new threat, researchers have developed multiple algorithms to detect synthetic images and identify their source generators. However, most existing source attribution techniques are designed to operate in a closed-set scenario, i.e. they can only be used to discriminate between known image generators. By contrast, new image-generation techniques are rapidly emerging. To contend with this, there is a great need for open-set source attribution techniques that can identify when synthetic images have originated from new, unseen generators. To address this problem, we propose a new metric learning-based approach. Our technique works by learning transferrable embeddings capable of discriminating between generators, even when they are not seen during training. An image is first assigned to a candidate generator, then is accepted or rejected based on its distance in the embedding space from known generators' learned reference points. Importantly, we identify that initializing our source attribution embedding network by pretraining it on image camera identification can improve our embeddings' transferability. Through a series of experiments, we demonstrate our approach's ability to attribute the source of synthetic images in open-set scenarios.